Covariance of stochastic integrals with respect to fractional Brownian motion

Yohaï Maayan; Eddy Mayer-Wolf

doi:10.1016/j.spa.2017.08.006

Covariance of stochastic integrals with respect to fractional Brownian motion

Yohaï Maayan, Eddy Mayer-Wolf

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a d-dimensional fractional Brownian motion (fBm) B_t with Hurst parameter H>[Formula presented], where the integrands are vector fields applied to B_t. It provides, for example, a direct alternative proof of Y. Hu and D. Nualart's result that the stochastic integral component in the fractional Bessel process decomposition is not itself a fractional Brownian motion.

Original language	English
Pages (from-to)	1635-1651
Number of pages	17
Journal	Stochastic Processes and their Applications
Volume	128
Issue number	5
DOIs	https://doi.org/10.1016/j.spa.2017.08.006
State	Published - May 2018

Keywords

Divergence integral
Fractional Bessel process
Fractional Brownian motion
Stochastic integral

All Science Journal Classification (ASJC) codes

Applied Mathematics
Statistics and Probability
Modelling and Simulation

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10.1016/j.spa.2017.08.006

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abstract = "We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a d-dimensional fractional Brownian motion (fBm) Bt with Hurst parameter H>[Formula presented], where the integrands are vector fields applied to Bt. It provides, for example, a direct alternative proof of Y. Hu and D. Nualart's result that the stochastic integral component in the fractional Bessel process decomposition is not itself a fractional Brownian motion.",

keywords = "Divergence integral, Fractional Bessel process, Fractional Brownian motion, Stochastic integral",

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T1 - Covariance of stochastic integrals with respect to fractional Brownian motion

AU - Maayan, Yohaï

AU - Mayer-Wolf, Eddy

PY - 2018/5

Y1 - 2018/5

N2 - We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a d-dimensional fractional Brownian motion (fBm) Bt with Hurst parameter H>[Formula presented], where the integrands are vector fields applied to Bt. It provides, for example, a direct alternative proof of Y. Hu and D. Nualart's result that the stochastic integral component in the fractional Bessel process decomposition is not itself a fractional Brownian motion.

AB - We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a d-dimensional fractional Brownian motion (fBm) Bt with Hurst parameter H>[Formula presented], where the integrands are vector fields applied to Bt. It provides, for example, a direct alternative proof of Y. Hu and D. Nualart's result that the stochastic integral component in the fractional Bessel process decomposition is not itself a fractional Brownian motion.

KW - Divergence integral

KW - Fractional Bessel process

KW - Fractional Brownian motion

KW - Stochastic integral

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U2 - 10.1016/j.spa.2017.08.006

DO - 10.1016/j.spa.2017.08.006

M3 - مقالة

SN - 0304-4149

VL - 128

SP - 1635

EP - 1651

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 5

ER -

Covariance of stochastic integrals with respect to fractional Brownian motion

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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